ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
In the case of nominally two-dimensional (2D) cylinders of arbitrary cross section in cross flow, the three-dimensionality of the wake manifests in the form of quasi-streamwise vortices. These three-dimensional (3D) features profoundly influence lift and drag forces. However, a two-dimensional projection of such a flow, where the effects of three-dimensionality are modeled, will be computationally very attractive. One can consider the two-dimensional projection as the limiting case of large eddy simulation, where the spanwise direction has been completely averaged out. The transport equation for the span-averaged spanwise component of vorticity, ω¯z, is considered; the 3D effects to be modeled appear as a subgrid scale flux of torque. It is shown that simple minded eddy viscosity type models that assume the flux vector to be proportional to the spatial gradient of ω¯z are inadequate. Here we extend the optimal modeling formalism [Moser, Balachandar, and Adrian, Turbulence and Internal Flow/Unsteady Aerodynamics and Hypersonics Conference, Annapolis, MD, pp. 269–274 (1998); Langford and Moser, J. Fluid Mech. 398, 321 (1999)] to address issues pertaining to complex flows with multiple directions of inhomogeneity. We present optimal closures for subgrid flux modeled in terms of ω¯z distribution, based on linear and quadratic stochastic approximations. These ideas are tested using the database of flow over a flat plate held normal to a cross flow. It is observed that even the optimal model has about 70% normalized error, indicating that the subgrid flux is only about 30% deterministic. Furthermore, it is observed that local models are inadequate, but there exists a region of nonlocality for model dependence, expanding beyond which does not improve the estimate. Higher order nonlinearities however do not seem to improve the model's predictability. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1321260
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